LMFDB - Embedded newform 325.3.w.e.24.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [325,3,Mod(24,325)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(325, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 7])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("325.24"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	325.w (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [40,0,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.85560859171$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			24.5
Character	$\chi$	$=$	325.24
Dual form			325.3.w.e.149.5

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.401493 - 0.107580i) q^{2} +(3.61165 - 2.08519i) q^{3} +(-3.31448 - 1.91361i) q^{4} +(-1.67438 + 0.448649i) q^{6} +(-10.0361 + 2.68917i) q^{7} +(2.30053 + 2.30053i) q^{8} +(4.19603 - 7.26773i) q^{9} +(-4.73818 - 1.26959i) q^{11} -15.9610 q^{12} +(-10.5948 + 7.53326i) q^{13} +4.31874 q^{14} +(6.97830 + 12.0868i) q^{16} +(11.0538 - 19.1458i) q^{17} +(-2.46654 + 2.46654i) q^{18} +(-33.5167 + 8.98078i) q^{19} +(-30.6396 + 30.6396i) q^{21} +(1.76576 + 1.01946i) q^{22} +(-15.9694 - 27.6598i) q^{23} +(13.1058 + 3.51168i) q^{24} +(5.06417 - 1.88476i) q^{26} +2.53538i q^{27} +(38.4106 + 10.2921i) q^{28} +(13.5241 + 23.4245i) q^{29} +(9.08360 + 9.08360i) q^{31} +(-4.86966 - 18.1738i) q^{32} +(-19.7600 + 5.29467i) q^{33} +(-6.49775 + 6.49775i) q^{34} +(-27.8153 + 16.0592i) q^{36} +(3.85300 - 14.3796i) q^{37} +14.4229 q^{38} +(-22.5565 + 49.2997i) q^{39} +(-3.69614 + 13.7942i) q^{41} +(15.5978 - 9.00539i) q^{42} +(2.96708 - 5.13914i) q^{43} +(13.2751 + 13.2751i) q^{44} +(3.43597 + 12.8232i) q^{46} +(-33.5097 - 33.5097i) q^{47} +(50.4064 + 29.1022i) q^{48} +(51.0571 - 29.4778i) q^{49} -92.1974i q^{51} +(49.5320 - 4.69442i) q^{52} -33.8049i q^{53} +(0.272755 - 1.01794i) q^{54} +(-29.2749 - 16.9019i) q^{56} +(-102.324 + 102.324i) q^{57} +(-2.90985 - 10.8597i) q^{58} +(-9.82174 - 36.6552i) q^{59} +(-9.55739 + 16.5539i) q^{61} +(-2.66979 - 4.62422i) q^{62} +(-22.5677 + 84.2237i) q^{63} -48.0059i q^{64} +8.50311 q^{66} +(-43.6377 - 11.6927i) q^{67} +(-73.2755 + 42.3056i) q^{68} +(-115.352 - 66.5984i) q^{69} +(-63.4555 + 17.0028i) q^{71} +(26.3727 - 7.06654i) q^{72} +(-55.4200 - 55.4200i) q^{73} +(-3.09391 + 5.35881i) q^{74} +(128.276 + 34.3715i) q^{76} +50.9671 q^{77} +(14.3600 - 17.3669i) q^{78} -71.0406 q^{79} +(43.0510 + 74.5665i) q^{81} +(2.96795 - 5.14064i) q^{82} +(54.0196 - 54.0196i) q^{83} +(160.187 - 42.9219i) q^{84} +(-1.74413 + 1.74413i) q^{86} +(97.6891 + 56.4008i) q^{87} +(-7.97958 - 13.8210i) q^{88} +(66.8590 + 17.9148i) q^{89} +(86.0727 - 104.096i) q^{91} +122.237i q^{92} +(51.7478 + 13.8658i) q^{93} +(9.84896 + 17.0589i) q^{94} +(-55.4833 - 55.4833i) q^{96} +(-14.8307 - 55.3488i) q^{97} +(-23.6703 + 6.34244i) q^{98} +(-29.1086 + 29.1086i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 12 q^{3} - 12 q^{6} - 44 q^{7} + 36 q^{8} + 72 q^{9} - 12 q^{11} + 120 q^{12} - 36 q^{13} - 48 q^{14} + 128 q^{16} - 32 q^{17} + 136 q^{18} - 68 q^{19} - 48 q^{21} - 72 q^{22} - 28 q^{23} + 56 q^{24}+ \cdots + 76 q^{99}+O(q^{100}) $ 40 * q - 12 * q^3 - 12 * q^6 - 44 * q^7 + 36 * q^8 + 72 * q^9 - 12 * q^11 + 120 * q^12 - 36 * q^13 - 48 * q^14 + 128 * q^16 - 32 * q^17 + 136 * q^18 - 68 * q^19 - 48 * q^21 - 72 * q^22 - 28 * q^23 + 56 * q^24 - 84 * q^26 + 76 * q^28 - 28 * q^29 + 128 * q^31 + 84 * q^32 - 68 * q^33 + 28 * q^34 + 300 * q^36 - 260 * q^37 + 8 * q^38 + 88 * q^39 + 68 * q^41 - 480 * q^42 + 32 * q^43 + 240 * q^44 + 260 * q^46 - 152 * q^47 - 480 * q^48 + 132 * q^49 + 488 * q^52 - 152 * q^54 - 288 * q^56 + 252 * q^57 + 468 * q^58 - 492 * q^59 - 100 * q^61 - 8 * q^62 - 356 * q^63 - 456 * q^66 - 56 * q^67 + 12 * q^68 + 576 * q^69 - 132 * q^71 + 396 * q^72 - 424 * q^73 + 160 * q^74 - 992 * q^76 + 344 * q^77 + 12 * q^78 + 248 * q^79 + 248 * q^82 - 112 * q^83 - 1100 * q^84 + 852 * q^86 - 1068 * q^87 + 8 * q^88 - 168 * q^89 - 160 * q^91 - 24 * q^93 - 328 * q^94 + 124 * q^96 + 1020 * q^97 + 1404 * q^98 + 76 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$-1$	$e\left(\frac{7}{12}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.401493	−	0.107580i	−0.200747	−	0.0537899i	0.157045	−	0.987592i	$-0.449803\pi$
$2$	−0.401493	−	0.107580i	−0.200747	−	0.0537899i	−0.357791	+	0.933802i	$0.616470\pi$
$3$	3.61165	−	2.08519i	1.20388	−	0.695063i	0.242468	−	0.970159i	$-0.422043\pi$
$3$	3.61165	−	2.08519i	1.20388	−	0.695063i	0.961417	+	0.275096i	$0.0887098\pi$
$4$	−3.31448	−	1.91361i	−0.828620	−	0.478404i
$5$		0			0
$5$		0			0
$6$	−1.67438	+	0.448649i	−0.279063	+	0.0747748i
$7$	−10.0361	+	2.68917i	−1.43373	+	0.384168i	−0.890335	−	0.455307i	$-0.849530\pi$
$7$	−10.0361	+	2.68917i	−1.43373	+	0.384168i	−0.543399	+	0.839475i	$0.682863\pi$
$8$	2.30053	+	2.30053i	0.287566	+	0.287566i
$9$	4.19603	−	7.26773i	0.466225	−	0.807526i
$10$		0			0
$11$	−4.73818	−	1.26959i	−0.430743	−	0.115417i	0.0369317	−	0.999318i	$-0.488242\pi$
$11$	−4.73818	−	1.26959i	−0.430743	−	0.115417i	−0.467675	+	0.883900i	$0.654908\pi$
$12$	−15.9610			−1.33008
$13$	−10.5948	+	7.53326i	−0.814986	+	0.579481i
$13$	−10.5948	+	7.53326i	−0.814986	+	0.579481i
$14$	4.31874			0.308482
$15$		0			0
$16$	6.97830	+	12.0868i	0.436144	+	0.755423i
$17$	11.0538	−	19.1458i	0.650226	−	1.12622i	−0.332842	−	0.942983i	$-0.608007\pi$
$17$	11.0538	−	19.1458i	0.650226	−	1.12622i	0.983068	−	0.183242i	$-0.0586592\pi$
$18$	−2.46654	+	2.46654i	−0.137030	+	0.137030i
$19$	−33.5167	+	8.98078i	−1.76404	+	0.472672i	−0.987529	−	0.157435i	$-0.949678\pi$
$19$	−33.5167	+	8.98078i	−1.76404	+	0.472672i	−0.776508	+	0.630107i	$0.783011\pi$
$20$		0			0
$21$	−30.6396	+	30.6396i	−1.45903	+	1.45903i
$22$	1.76576	+	1.01946i	0.0802620	+	0.0463393i
$23$	−15.9694	−	27.6598i	−0.694321	−	1.20260i	−0.970409	−	0.241467i	$-0.922372\pi$
$23$	−15.9694	−	27.6598i	−0.694321	−	1.20260i	0.276088	−	0.961132i	$-0.410962\pi$
$24$	13.1058	+	3.51168i	0.546073	+	0.146320i
$25$		0			0
$26$	5.06417	−	1.88476i	0.194776	−	0.0724909i
$27$			2.53538i			0.0939028i
$28$	38.4106	+	10.2921i	1.37181	+	0.367574i
$29$	13.5241	+	23.4245i	0.466350	+	0.807742i	0.999261	−	0.0384292i	$-0.0122354\pi$
$29$	13.5241	+	23.4245i	0.466350	+	0.807742i	−0.532911	+	0.846171i	$0.678902\pi$
$30$		0			0
$31$	9.08360	+	9.08360i	0.293019	+	0.293019i	0.838272	−	0.545253i	$-0.183566\pi$
$31$	9.08360	+	9.08360i	0.293019	+	0.293019i	−0.545253	+	0.838272i	$0.683566\pi$
$32$	−4.86966	−	18.1738i	−0.152177	−	0.567932i
$33$	−19.7600	+	5.29467i	−0.598788	+	0.160445i
$34$	−6.49775	+	6.49775i	−0.191110	+	0.191110i
$35$		0			0
$36$	−27.8153	+	16.0592i	−0.772646	+	0.446088i
$37$	3.85300	−	14.3796i	0.104135	−	0.388638i	−0.894110	−	0.447846i	$-0.852191\pi$
$37$	3.85300	−	14.3796i	0.104135	−	0.388638i	0.998246	+	0.0592089i	$0.0188578\pi$
$38$	14.4229			0.379550
$39$	−22.5565	+	49.2997i	−0.578373	+	1.26409i
$40$		0			0
$41$	−3.69614	+	13.7942i	−0.0901497	+	0.336443i	−0.996240	−	0.0866421i	$-0.972386\pi$
$41$	−3.69614	+	13.7942i	−0.0901497	+	0.336443i	0.906090	+	0.423085i	$0.139053\pi$
$42$	15.5978	−	9.00539i	0.371376	−	0.214414i
$43$	2.96708	−	5.13914i	0.0690019	−	0.119515i	−0.829460	−	0.558566i	$-0.811352\pi$
$43$	2.96708	−	5.13914i	0.0690019	−	0.119515i	0.898462	+	0.439051i	$0.144685\pi$
$44$	13.2751	+	13.2751i	0.301706	+	0.301706i
$45$		0			0
$46$	3.43597	+	12.8232i	0.0746949	+	0.278765i
$47$	−33.5097	−	33.5097i	−0.712973	−	0.712973i	0.254183	−	0.967156i	$-0.418193\pi$
$47$	−33.5097	−	33.5097i	−0.712973	−	0.712973i	−0.967156	+	0.254183i	$0.918193\pi$
$48$	50.4064	+	29.1022i	1.05013	+	0.606295i
$49$	51.0571	−	29.4778i	1.04198	−	0.601588i
$50$		0			0
$51$		−	92.1974i		−	1.80779i
$52$	49.5320	−	4.69442i	0.952539	−	0.0902772i
$53$		−	33.8049i		−	0.637829i	−0.947784	−	0.318914i	$-0.896682\pi$
$53$		−	33.8049i		−	0.637829i	0.947784	−	0.318914i	$-0.103318\pi$
$54$	0.272755	−	1.01794i	0.00505102	−	0.0188507i
$55$		0			0
$56$	−29.2749	−	16.9019i	−0.522767	−	0.301820i
$57$	−102.324	+	102.324i	−1.79516	+	1.79516i
$58$	−2.90985	−	10.8597i	−0.0501699	−	0.187236i
$59$	−9.82174	−	36.6552i	−0.166470	−	0.621275i	−0.997848	−	0.0655678i	$-0.979114\pi$
$59$	−9.82174	−	36.6552i	−0.166470	−	0.621275i	0.831378	−	0.555707i	$-0.187553\pi$
$60$		0			0
$61$	−9.55739	+	16.5539i	−0.156678	+	0.271375i	−0.933669	−	0.358137i	$-0.883412\pi$
$61$	−9.55739	+	16.5539i	−0.156678	+	0.271375i	0.776990	+	0.629512i	$0.216745\pi$
$62$	−2.66979	−	4.62422i	−0.0430612	−	0.0745841i
$63$	−22.5677	+	84.2237i	−0.358217	+	1.33688i
$64$		−	48.0059i		−	0.750092i
$65$		0			0
$66$	8.50311			0.128835
$67$	−43.6377	−	11.6927i	−0.651308	−	0.174518i	−0.0819881	−	0.996633i	$-0.526127\pi$
$67$	−43.6377	−	11.6927i	−0.651308	−	0.174518i	−0.569320	+	0.822116i	$0.692794\pi$
$68$	−73.2755	+	42.3056i	−1.07758	+	0.622141i
$69$	−115.352	−	66.5984i	−1.67176	−	0.965193i
$70$		0			0
$71$	−63.4555	+	17.0028i	−0.893739	+	0.239477i	−0.676325	−	0.736603i	$-0.736429\pi$
$71$	−63.4555	+	17.0028i	−0.893739	+	0.239477i	−0.217414	+	0.976080i	$0.569762\pi$
$72$	26.3727	−	7.06654i	0.366288	−	0.0981465i
$73$	−55.4200	−	55.4200i	−0.759178	−	0.759178i	0.216995	−	0.976173i	$-0.430375\pi$
$73$	−55.4200	−	55.4200i	−0.759178	−	0.759178i	−0.976173	+	0.216995i	$0.930375\pi$
$74$	−3.09391	+	5.35881i	−0.0418096	+	0.0724163i
$75$		0			0
$76$	128.276	+	34.3715i	1.68784	+	0.452257i
$77$	50.9671			0.661911
$78$	14.3600	−	17.3669i	0.184102	−	0.222652i
$79$	−71.0406			−0.899249			−0.449624	−	0.893218i	$-0.648442\pi$
$79$	−71.0406			−0.899249			−0.449624	+	0.893218i	$0.648442\pi$
$80$		0			0
$81$	43.0510	+	74.5665i	0.531493	+	0.920574i
$82$	2.96795	−	5.14064i	0.0361945	−	0.0626908i
$83$	54.0196	−	54.0196i	0.650839	−	0.650839i	−0.302356	−	0.953195i	$-0.597773\pi$
$83$	54.0196	−	54.0196i	0.650839	−	0.650839i	0.953195	+	0.302356i	$0.0977732\pi$
$84$	160.187	−	42.9219i	1.90698	−	0.510975i
$85$		0			0
$86$	−1.74413	+	1.74413i	−0.0202806	+	0.0202806i
$87$	97.6891	+	56.4008i	1.12286	+	0.648285i
$88$	−7.97958	−	13.8210i	−0.0906771	−	0.157057i
$89$	66.8590	+	17.9148i	0.751225	+	0.201290i	0.614061	−	0.789258i	$-0.289535\pi$
$89$	66.8590	+	17.9148i	0.751225	+	0.201290i	0.137164	+	0.990548i	$0.456201\pi$
$90$		0			0
$91$	86.0727	−	104.096i	0.945854	−	1.14391i
$92$			122.237i			1.32866i
$93$	51.7478	+	13.8658i	0.556428	+	0.149094i
$94$	9.84896	+	17.0589i	0.104776	+	0.181478i
$95$		0			0
$96$	−55.4833	−	55.4833i	−0.577951	−	0.577951i
$97$	−14.8307	−	55.3488i	−0.152893	−	0.570606i	−0.999277	−	0.0380317i	$-0.987891\pi$
$97$	−14.8307	−	55.3488i	−0.152893	−	0.570606i	0.846383	−	0.532575i	$-0.178775\pi$
$98$	−23.6703	+	6.34244i	−0.241534	+	0.0647188i
$99$	−29.1086	+	29.1086i	−0.294026	+	0.294026i
$100$		0			0
$101$	93.0587	−	53.7275i	0.921374	−	0.531955i	0.0373006	−	0.999304i	$-0.488124\pi$
$101$	93.0587	−	53.7275i	0.921374	−	0.531955i	0.884073	+	0.467349i	$0.154791\pi$
$102$	−9.91859	+	37.0167i	−0.0972410	+	0.362908i
$103$	−67.5550			−0.655873			−0.327937	−	0.944700i	$-0.606353\pi$
$103$	−67.5550			−0.655873			−0.327937	+	0.944700i	$0.606353\pi$
$104$	−41.7042	−	7.04320i	−0.401001	−	0.0677231i
$105$		0			0
$106$	−3.63673	+	13.5725i	−0.0343088	+	0.128042i
$107$	139.927	−	80.7868i	1.30773	−	0.755017i	0.326012	−	0.945366i	$-0.394295\pi$
$107$	139.927	−	80.7868i	1.30773	−	0.755017i	0.981717	+	0.190349i	$0.0609618\pi$
$108$	4.85173	−	8.40345i	0.0449234	−	0.0778097i
$109$	38.4204	+	38.4204i	0.352481	+	0.352481i	0.861032	−	0.508551i	$-0.169819\pi$
$109$	38.4204	+	38.4204i	0.352481	+	0.352481i	−0.508551	+	0.861032i	$0.669819\pi$
$110$		0			0
$111$	−16.0685	−	59.9683i	−0.144761	−	0.540255i
$112$	−102.539	−	102.539i	−0.915523	−	0.915523i
$113$	−76.7296	−	44.2999i	−0.679023	−	0.392034i	0.120464	−	0.992718i	$-0.461562\pi$
$113$	−76.7296	−	44.2999i	−0.679023	−	0.392034i	−0.799487	+	0.600684i	$0.794895\pi$
$114$	52.0905	−	30.0745i	0.456934	−	0.263811i
$115$		0			0
$116$		−	103.520i		−	0.892414i
$117$	10.2936	+	108.610i	0.0879791	+	0.928290i
$118$			15.7735i			0.133673i
$119$	−59.4514	+	221.876i	−0.499592	+	1.86450i
$120$		0			0
$121$	−83.9506	−	48.4689i	−0.693807	−	0.400569i
$122$	5.61809	−	5.61809i	0.0460499	−	0.0460499i
$123$	15.4143	+	57.5269i	0.125319	+	0.467699i
$124$	−12.7249	−	47.4899i	−0.102620	−	0.382983i
$125$		0			0
$126$	18.1216	−	31.3875i	0.143822	−	0.249107i
$127$	76.9754	+	133.325i	0.606105	+	1.04981i	0.991876	+	0.127210i	$0.0406024\pi$
$127$	76.9754	+	133.325i	0.606105	+	1.04981i	−0.385770	+	0.922595i	$0.626064\pi$
$128$	−24.6431	+	91.9693i	−0.192524	+	0.718510i
$129$		−	24.7477i		−	0.191843i
$130$		0			0
$131$	144.341			1.10184			0.550919	−	0.834559i	$-0.314277\pi$
$131$	144.341			1.10184			0.550919	+	0.834559i	$0.314277\pi$
$132$	75.6260	+	20.2639i	0.572924	+	0.153515i
$133$	312.227	−	180.265i	2.34757	−	1.35537i
$134$	16.2623	+	9.38907i	0.121361	+	0.0700677i
$135$		0			0
$136$	69.4752	−	18.6158i	0.510847	−	0.136881i
$137$	91.9804	−	24.6461i	0.671390	−	0.179898i	0.0930090	−	0.995665i	$-0.470351\pi$
$137$	91.9804	−	24.6461i	0.671390	−	0.179898i	0.578381	+	0.815767i	$0.303685\pi$
$138$	39.1483	+	39.1483i	0.283683	+	0.283683i
$139$	40.5417	−	70.2202i	0.291667	−	0.505182i	−0.682537	−	0.730851i	$-0.739124\pi$
$139$	40.5417	−	70.2202i	0.291667	−	0.505182i	0.974204	+	0.225669i	$0.0724568\pi$
$140$		0			0
$141$	−190.900	−	51.1514i	−1.35390	−	0.362776i
$142$	27.3061			0.192297
$143$	59.7643	−	22.2428i	0.417932	−	0.155544i
$144$	117.125			0.813365
$145$		0			0
$146$	16.2887	+	28.2128i	0.111566	+	0.193239i
$147$	122.934	−	212.927i	0.836283	−	1.44849i
$148$	−40.2877	+	40.2877i	−0.272214	+	0.272214i
$149$	5.37626	−	1.44056i	0.0360823	−	0.00966821i	−0.240733	−	0.970591i	$-0.577388\pi$
$149$	5.37626	−	1.44056i	0.0360823	−	0.00966821i	0.276815	+	0.960923i	$0.410721\pi$
$150$		0			0
$151$	−139.922	+	139.922i	−0.926637	+	0.926637i	−0.997487	−	0.0708501i	$-0.977429\pi$
$151$	−139.922	+	139.922i	−0.926637	+	0.926637i	0.0708501	+	0.997487i	$0.477429\pi$
$152$	−97.7667	−	56.4456i	−0.643202	−	0.371353i
$153$	−92.7644	−	160.673i	−0.606304	−	1.05015i
$154$	−20.4630	−	5.48304i	−0.132876	−	0.0356041i
$155$		0			0
$156$	169.104	−	120.238i	1.08400	−	0.770758i
$157$			18.3651i			0.116975i	0.998288	+	0.0584877i	$0.0186278\pi$
$157$			18.3651i			0.116975i	−0.998288	+	0.0584877i	$0.981372\pi$
$158$	28.5224	+	7.64254i	0.180521	+	0.0483705i
$159$	−70.4897	−	122.092i	−0.443331	−	0.767872i
$160$		0			0
$161$	234.653	+	234.653i	1.45747	+	1.45747i
$162$	−9.26283	−	34.5694i	−0.0571780	−	0.213391i
$163$	61.7407	−	16.5434i	0.378777	−	0.101493i	−0.0644066	−	0.997924i	$-0.520515\pi$
$163$	61.7407	−	16.5434i	0.378777	−	0.101493i	0.443184	+	0.896431i	$0.353849\pi$
$164$	38.6475	−	38.6475i	0.235656	−	0.235656i
$165$		0			0
$166$	−27.5000	+	15.8771i	−0.165662	+	0.0956452i
$167$	−66.9870	+	249.999i	−0.401120	+	1.49700i	0.409981	+	0.912094i	$0.365535\pi$
$167$	−66.9870	+	249.999i	−0.401120	+	1.49700i	−0.811101	+	0.584906i	$0.801131\pi$
$168$	−140.975			−0.839134
$169$	55.5001	−	159.627i	0.328403	−	0.944538i
$170$		0			0
$171$	−75.3671	+	281.274i	−0.440744	+	1.64488i
$172$	−19.6687	+	11.3557i	−0.114353	+	0.0660215i
$173$	−141.601	+	245.260i	−0.818503	+	1.41769i	0.0882824	+	0.996095i	$0.471862\pi$
$173$	−141.601	+	245.260i	−0.818503	+	1.41769i	−0.906785	+	0.421593i	$0.861471\pi$
$174$	−33.1539	−	33.1539i	−0.190540	−	0.190540i
$175$		0			0
$176$	−17.7192	−	66.1289i	−0.100677	−	0.375732i
$177$	−111.906	−	111.906i	−0.632236	−	0.632236i
$178$	−24.9162	−	14.3854i	−0.139979	−	0.0808167i
$179$	−271.813	+	156.932i	−1.51851	+	0.876713i	−0.518748	+	0.854927i	$0.673602\pi$
$179$	−271.813	+	156.932i	−1.51851	+	0.876713i	−0.999763	+	0.0217855i	$0.993065\pi$
$180$		0			0
$181$		−	296.950i		−	1.64061i	−0.571928	−	0.820304i	$-0.693804\pi$
$181$		−	296.950i		−	1.64061i	0.571928	−	0.820304i	$-0.306196\pi$
$182$	−45.7563	+	32.5342i	−0.251408	+	0.178759i
$183$			79.7158i			0.435606i
$184$	26.8941	−	100.370i	0.146164	−	0.545490i
$185$		0			0
$186$	−19.2847	−	11.1340i	−0.103681	−	0.0598604i
$187$	−76.6824	+	76.6824i	−0.410067	+	0.410067i
$188$	46.9425	+	175.192i	0.249694	+	0.931872i
$189$	−6.81807	−	25.4454i	−0.0360744	−	0.134632i
$190$		0			0
$191$	−156.806	+	271.595i	−0.820972	+	1.42197i	0.0839866	+	0.996467i	$0.473235\pi$
$191$	−156.806	+	271.595i	−0.820972	+	1.42197i	−0.904959	+	0.425499i	$0.860099\pi$
$192$	−100.101	−	173.381i	−0.521361	−	0.903024i
$193$	23.3090	−	86.9902i	0.120772	−	0.450726i	−0.878882	−	0.477039i	$-0.841710\pi$
$193$	23.3090	−	86.9902i	0.120772	−	0.450726i	0.999654	+	0.0263129i	$0.00837662\pi$
$194$			23.8177i			0.122771i
$195$		0			0
$196$	−225.637			−1.15121
$197$	−40.1857	−	10.7677i	−0.203989	−	0.0546586i	0.155378	−	0.987855i	$-0.450340\pi$
$197$	−40.1857	−	10.7677i	−0.203989	−	0.0546586i	−0.359366	+	0.933197i	$0.617007\pi$
$198$	14.8184	−	8.55540i	0.0748403	−	0.0432091i
$199$	108.739	+	62.7807i	0.546429	+	0.315481i	0.747681	−	0.664059i	$-0.231167\pi$
$199$	108.739	+	62.7807i	0.546429	+	0.315481i	−0.201251	+	0.979540i	$0.564501\pi$
$200$		0			0
$201$	−181.986	+	48.7629i	−0.905401	+	0.242601i
$202$	−43.1425	+	11.5600i	−0.213577	+	0.0572277i
$203$	−198.723	−	198.723i	−0.978930	−	0.978930i
$204$	−176.430	+	305.586i	−0.864855	+	1.49797i
$205$		0			0
$206$	27.1229	+	7.26755i	0.131664	+	0.0352794i
$207$	−268.032			−1.29484
$208$	−164.987	−	75.4878i	−0.793205	−	0.362922i
$209$	170.210			0.814402
$210$		0			0
$211$	−117.742	−	203.935i	−0.558018	−	0.966515i	−0.997662	−	0.0683431i	$-0.978229\pi$
$211$	−117.742	−	203.935i	−0.558018	−	0.966515i	0.439644	−	0.898172i	$-0.355105\pi$
$212$	−64.6896	+	112.046i	−0.305140	+	0.528517i
$213$	−193.725	+	193.725i	−0.909507	+	0.909507i
$214$	−64.8708	+	17.3821i	−0.303134	+	0.0812246i
$215$		0			0
$216$	−5.83271	+	5.83271i	−0.0270033	+	0.0270033i
$217$	−115.592	−	66.7368i	−0.532680	−	0.307543i
$218$	−11.2923	−	19.5588i	−0.0517995	−	0.0897193i
$219$	−315.719	−	84.5967i	−1.44164	−	0.386286i
$220$		0			0
$221$	27.1169	+	286.118i	0.122701	+	1.29465i
$222$			25.8055i			0.116241i
$223$	203.738	+	54.5913i	0.913621	+	0.244804i	0.684857	−	0.728678i	$-0.259865\pi$
$223$	203.738	+	54.5913i	0.913621	+	0.244804i	0.228765	+	0.973482i	$0.426531\pi$
$224$	97.7451	+	169.299i	0.436362	+	0.755801i
$225$		0			0
$226$	26.0407	+	26.0407i	0.115224	+	0.115224i
$227$	−26.3713	−	98.4190i	−0.116173	−	0.433564i	0.883199	−	0.468999i	$-0.155385\pi$
$227$	−26.3713	−	98.4190i	−0.116173	−	0.433564i	−0.999372	+	0.0354349i	$0.988718\pi$
$228$	534.960	−	143.342i	2.34632	−	0.628694i
$229$	−106.435	+	106.435i	−0.464784	+	0.464784i	−0.900220	−	0.435436i	$-0.856594\pi$
$229$	−106.435	+	106.435i	−0.464784	+	0.464784i	0.435436	+	0.900220i	$0.356594\pi$
$230$		0			0
$231$	184.076	−	106.276i	0.796864	−	0.460070i
$232$	−22.7761	+	85.0015i	−0.0981728	+	0.366386i
$233$	−339.132			−1.45550			−0.727751	−	0.685841i	$-0.759434\pi$
$233$	−339.132			−1.45550			−0.727751	+	0.685841i	$0.759434\pi$
$234$	7.55145	−	44.7136i	0.0322712	−	0.191084i
$235$		0			0
$236$	−37.5901	+	140.288i	−0.159280	+	0.594441i
$237$	−256.574	+	148.133i	−1.08259	+	0.625034i
$238$	47.7387	−	82.6859i	0.200583	−	0.347420i
$239$	201.648	+	201.648i	0.843716	+	0.843716i	0.989340	−	0.145624i	$-0.0465189\pi$
$239$	201.648	+	201.648i	0.843716	+	0.843716i	−0.145624	+	0.989340i	$0.546519\pi$
$240$		0			0
$241$	70.3423	+	262.521i	0.291877	+	1.08930i	0.943666	+	0.330899i	$0.107352\pi$
$241$	70.3423	+	262.521i	0.291877	+	1.08930i	−0.651790	+	0.758400i	$0.725982\pi$
$242$	28.4913	+	28.4913i	0.117733	+	0.117733i
$243$	291.209	+	168.130i	1.19839	+	0.691891i
$244$	63.3555	−	36.5783i	0.259654	−	0.149911i
$245$		0			0
$246$		−	24.7550i		−	0.100630i
$247$	287.449	−	347.640i	1.16376	−	1.40745i
$248$			41.7942i			0.168525i
$249$	82.4590	−	307.741i	0.331161	−	1.23591i
$250$		0			0
$251$	−215.498	−	124.418i	−0.858560	−	0.495690i	0.00497011	−	0.999988i	$-0.498418\pi$
$251$	−215.498	−	124.418i	−0.858560	−	0.495690i	−0.863530	+	0.504298i	$0.831751\pi$
$252$	235.972	−	235.972i	0.936396	−	0.936396i
$253$	40.5492	+	151.332i	0.160273	+	0.598148i
$254$	−16.5620	−	61.8102i	−0.0652047	−	0.243347i
$255$		0			0
$256$	−76.2237	+	132.023i	−0.297749	+	0.515716i
$257$	−145.517	−	252.043i	−0.566214	−	0.980712i	−0.996936	−	0.0782267i	$-0.975074\pi$
$257$	−145.517	−	252.043i	−0.566214	−	0.980712i	0.430721	−	0.902485i	$-0.358259\pi$
$258$	−2.66235	+	9.93604i	−0.0103192	+	0.0385118i
$259$			154.677i			0.597208i
$260$		0			0
$261$	226.991			0.869696
$262$	−57.9519	−	15.5282i	−0.221190	−	0.0592678i
$263$	2.53571	−	1.46399i	0.00964148	−	0.00556651i	−0.495172	−	0.868795i	$-0.664895\pi$
$263$	2.53571	−	1.46399i	0.00964148	−	0.00556651i	0.504813	+	0.863229i	$0.331561\pi$
$264$	−57.6390	−	33.2779i	−0.218329	−	0.126053i
$265$		0			0
$266$	−144.750	+	38.7857i	−0.544173	+	0.145811i
$267$	278.827	−	74.7116i	1.04430	−	0.279819i
$268$	122.261	+	122.261i	0.456197	+	0.456197i
$269$	−66.7468	+	115.609i	−0.248129	+	0.429773i	−0.963007	−	0.269477i	$-0.913149\pi$
$269$	−66.7468	+	115.609i	−0.248129	+	0.429773i	0.714877	+	0.699250i	$0.246482\pi$
$270$		0			0
$271$	−450.750	−	120.778i	−1.66329	−	0.445676i	−0.699997	−	0.714145i	$-0.746816\pi$
$271$	−450.750	−	120.778i	−1.66329	−	0.445676i	−0.963288	+	0.268469i	$0.913482\pi$
$272$	308.548			1.13437
$273$	93.8049	−	555.437i	0.343608	−	2.03457i
$274$	−39.5809			−0.144456
$275$		0			0
$276$	254.887	+	441.478i	0.923504	+	1.59956i
$277$	−67.7968	+	117.428i	−0.244754	+	0.423926i	−0.962062	−	0.272829i	$-0.912041\pi$
$277$	−67.7968	+	117.428i	−0.244754	+	0.423926i	0.717308	+	0.696756i	$0.245374\pi$
$278$	−23.8315	+	23.8315i	−0.0857248	+	0.0857248i
$279$	104.132	−	27.9021i	0.373233	−	0.100008i
$280$		0			0
$281$	354.240	−	354.240i	1.26064	−	1.26064i	0.309856	−	0.950784i	$-0.399719\pi$
$281$	354.240	−	354.240i	1.26064	−	1.26064i	0.950784	−	0.309856i	$-0.100281\pi$
$282$	71.1421	+	41.0739i	0.252277	+	0.145652i
$283$	−29.2582	−	50.6767i	−0.103386	−	0.179070i	0.809692	−	0.586856i	$-0.199634\pi$
$283$	−29.2582	−	50.6767i	−0.103386	−	0.179070i	−0.913078	+	0.407786i	$0.866301\pi$
$284$	242.859	+	65.0738i	0.855136	+	0.229133i
$285$		0			0
$286$	−26.3878	+	2.50092i	−0.0922652	+	0.00874447i
$287$		−	148.380i		−	0.517003i
$288$	−152.516	−	40.8664i	−0.529568	−	0.141897i
$289$	−99.8751	−	172.989i	−0.345588	−	0.598577i
$290$		0			0
$291$	−168.976	−	168.976i	−0.580673	−	0.580673i
$292$	77.6359	+	289.741i	0.265876	+	0.992264i
$293$	4.38016	−	1.17366i	0.0149493	−	0.00400566i	−0.251337	−	0.967900i	$-0.580870\pi$
$293$	4.38016	−	1.17366i	0.0149493	−	0.00400566i	0.266286	+	0.963894i	$0.414203\pi$
$294$	−72.2637	+	72.2637i	−0.245795	+	0.245795i
$295$		0			0
$296$	41.9446	−	24.2167i	0.141705	−	0.0818133i
$297$	3.21889	−	12.0131i	0.0108380	−	0.0404480i
$298$	−2.31351			−0.00776345
$299$	377.561	+	172.749i	1.26275	+	0.577755i
$300$		0			0
$301$	−15.9580	+	59.5561i	−0.0530166	+	0.197861i
$302$	71.2306	−	41.1250i	0.235863	−	0.136176i
$303$	224.064	−	388.090i	0.739485	−	1.28083i
$304$	−342.438	−	342.438i	−1.12644	−	1.12644i
$305$		0			0
$306$	19.9592	+	74.4886i	0.0652260	+	0.243427i
$307$	174.089	+	174.089i	0.567066	+	0.567066i	0.931305	−	0.364240i	$-0.118671\pi$
$307$	174.089	+	174.089i	0.567066	+	0.567066i	−0.364240	+	0.931305i	$0.618671\pi$
$308$	−168.929	−	97.5315i	−0.548472	−	0.316661i
$309$	−243.985	+	140.865i	−0.789596	+	0.455873i
$310$		0			0
$311$			162.502i			0.522513i	0.965269	+	0.261256i	$0.0841368\pi$
$311$			162.502i			0.522513i	−0.965269	+	0.261256i	$0.915863\pi$
$312$	−165.307	+	61.5234i	−0.529831	+	0.197190i
$313$			308.073i			0.984259i	0.870522	+	0.492129i	$0.163781\pi$
$313$			308.073i			0.984259i	−0.870522	+	0.492129i	$0.836219\pi$
$314$	1.97572	−	7.37348i	0.00629209	−	0.0234824i
$315$		0			0
$316$	235.463	+	135.944i	0.745135	+	0.430204i
$317$	32.2149	−	32.2149i	0.101624	−	0.101624i	−0.654467	−	0.756091i	$-0.727107\pi$
$317$	32.2149	−	32.2149i	0.101624	−	0.101624i	0.756091	+	0.654467i	$0.227107\pi$
$318$	15.1665	+	56.6023i	0.0476935	+	0.177995i
$319$	−34.3403	−	128.160i	−0.107650	−	0.401754i
$320$		0			0
$321$	336.912	−	583.548i	1.04957	−	1.81791i
$322$	−68.9676	−	119.455i	−0.214185	−	0.370980i
$323$	−198.544	+	740.977i	−0.614688	+	2.29405i
$324$		−	329.532i		−	1.01707i
$325$		0			0
$326$	−26.5682			−0.0814976
$327$	218.875	+	58.6474i	0.669343	+	0.179350i
$328$	−40.2370	+	23.2308i	−0.122674	+	0.0708257i
$329$	426.421	+	246.195i	1.29611	+	0.748312i
$330$		0			0
$331$	113.219	−	30.3370i	0.342053	−	0.0916527i	−0.0837035	−	0.996491i	$-0.526675\pi$
$331$	113.219	−	30.3370i	0.342053	−	0.0916527i	0.425756	+	0.904838i	$0.360008\pi$
$332$	−282.420	+	75.6741i	−0.850662	+	0.227934i
$333$	−88.3397	−	88.3397i	−0.265284	−	0.265284i
$334$	53.7897	−	93.1665i	0.161047	−	0.278942i
$335$		0			0
$336$	−584.146	−	156.522i	−1.73853	−	0.465838i
$337$	−244.800			−0.726410			−0.363205	−	0.931709i	$-0.618318\pi$
$337$	−244.800			−0.726410			−0.363205	+	0.931709i	$0.618318\pi$
$338$	−39.4556	+	58.1184i	−0.116732	+	0.171948i
$339$	−369.494			−1.08995
$340$		0			0
$341$	−31.5072	−	54.5721i	−0.0923966	−	0.160036i
$342$	60.5188	−	104.822i	0.176956	−	0.306496i
$343$	−73.1436	+	73.1436i	−0.213247	+	0.213247i
$344$	18.6486	−	4.99688i	0.0542110	−	0.0145258i
$345$		0			0
$346$	83.2369	−	83.2369i	0.240569	−	0.240569i
$347$	−58.4467	−	33.7442i	−0.168434	−	0.0972456i	0.413413	−	0.910544i	$-0.364337\pi$
$347$	−58.4467	−	33.7442i	−0.168434	−	0.0972456i	−0.581847	+	0.813298i	$0.697670\pi$
$348$	−215.859	−	373.879i	−0.620284	−	1.07436i
$349$	410.314	+	109.943i	1.17568	+	0.315024i	0.793213	−	0.608944i	$-0.208407\pi$
$349$	410.314	+	109.943i	1.17568	+	0.315024i	0.382471	+	0.923968i	$0.375073\pi$
$350$		0			0
$351$	−19.0996	−	26.8618i	−0.0544149	−	0.0765294i
$352$			92.2932i			0.262197i
$353$	66.0052	+	17.6860i	0.186984	+	0.0501021i	0.351096	−	0.936340i	$-0.385809\pi$
$353$	66.0052	+	17.6860i	0.186984	+	0.0501021i	−0.164112	+	0.986442i	$0.552476\pi$
$354$	32.8906	+	56.9683i	0.0929114	+	0.160927i
$355$		0			0
$356$	−187.321	−	187.321i	−0.526182	−	0.526182i
$357$	247.935	+	925.306i	0.694496	+	2.59189i
$358$	126.014	−	33.7653i	0.351994	−	0.0943166i
$359$	−78.7225	+	78.7225i	−0.219283	+	0.219283i	−0.808196	−	0.588913i	$-0.799556\pi$
$359$	−78.7225	+	78.7225i	−0.219283	+	0.219283i	0.588913	+	0.808196i	$0.299556\pi$
$360$		0			0
$361$	730.081	−	421.512i	2.02238	−	1.16762i
$362$	−31.9458	+	119.223i	−0.0882482	+	0.329347i
$363$	−404.267			−1.11368
$364$	−484.486	+	180.314i	−1.33101	+	0.495368i
$365$		0			0
$366$	8.57581	−	32.0054i	0.0234312	−	0.0874464i
$367$	−161.382	+	93.1738i	−0.439732	+	0.253880i	−0.703484	−	0.710711i	$-0.748373\pi$
$367$	−161.382	+	93.1738i	−0.439732	+	0.253880i	0.263752	+	0.964591i	$0.415040\pi$
$368$	222.878	−	386.037i	0.605648	−	1.04901i
$369$	84.7433	+	84.7433i	0.229657	+	0.229657i
$370$		0			0
$371$	90.9073	+	339.271i	0.245033	+	0.914476i
$372$	−144.983	−	144.983i	−0.389740	−	0.389740i
$373$	131.058	+	75.6663i	0.351362	+	0.202859i	0.665285	−	0.746590i	$-0.268310\pi$
$373$	131.058	+	75.6663i	0.351362	+	0.202859i	−0.313923	+	0.949448i	$0.601643\pi$
$374$	39.0370	−	22.5380i	0.104377	−	0.0602621i
$375$		0			0
$376$		−	154.180i		−	0.410054i
$377$	−319.749	−	146.297i	−0.848140	−	0.388057i
$378$			10.9496i			0.0289673i
$379$	64.9460	−	242.382i	0.171362	−	0.639530i	−0.825781	−	0.563990i	$-0.809265\pi$
$379$	64.9460	−	242.382i	0.171362	−	0.639530i	0.997143	−	0.0755394i	$-0.0240679\pi$
$380$		0			0
$381$	556.017	+	321.016i	1.45936	+	0.842563i
$382$	92.1747	−	92.1747i	0.241295	−	0.241295i
$383$	9.26704	+	34.5851i	0.0241959	+	0.0903004i	0.976968	−	0.213386i	$-0.0684492\pi$
$383$	9.26704	+	34.5851i	0.0241959	+	0.0903004i	−0.952772	+	0.303686i	$0.901782\pi$
$384$	102.771	+	383.547i	0.267633	+	0.998819i
$385$		0			0
$386$	−18.7168	+	32.4184i	−0.0484891	+	0.0839855i
$387$	−24.8999	−	43.1279i	−0.0643409	−	0.111442i
$388$	−56.7604	+	211.833i	−0.146290	+	0.545960i
$389$			38.2987i			0.0984543i	0.998788	+	0.0492271i	$0.0156758\pi$
$389$			38.2987i			0.0984543i	−0.998788	+	0.0492271i	$0.984324\pi$
$390$		0			0
$391$	−706.092			−1.80586
$392$	185.273	+	49.6437i	0.472635	+	0.126642i
$393$	521.309	−	300.978i	1.32649	−	0.765847i
$394$	14.9759	+	8.64635i	0.0380099	+	0.0219451i
$395$		0			0
$396$	152.182	−	40.7771i	0.384299	−	0.102972i
$397$	160.341	−	42.9634i	0.403883	−	0.108220i	−0.0511582	−	0.998691i	$-0.516291\pi$
$397$	160.341	−	42.9634i	0.403883	−	0.108220i	0.455041	+	0.890471i	$0.349625\pi$
$398$	−36.9042	−	36.9042i	−0.0927242	−	0.0927242i
$399$	751.771	−	1302.11i	1.88414	−	3.26342i
$400$		0			0
$401$	−94.1630	−	25.2309i	−0.234820	−	0.0629199i	0.139490	−	0.990224i	$-0.455454\pi$
$401$	−94.1630	−	25.2309i	−0.234820	−	0.0629199i	−0.374310	+	0.927304i	$0.622120\pi$
$402$	78.3119			0.194806
$403$	−164.668	−	27.8100i	−0.408606	−	0.0690073i
$404$	−411.255			−1.01796
$405$		0			0
$406$	58.4073	+	101.164i	0.143860	+	0.249174i
$407$	−36.5124	+	63.2413i	−0.0897110	+	0.155384i
$408$	212.103	−	212.103i	0.519860	−	0.519860i
$409$	−647.053	+	173.377i	−1.58204	+	0.423905i	−0.939556	−	0.342396i	$-0.888762\pi$
$409$	−647.053	+	173.377i	−1.58204	+	0.423905i	−0.642481	+	0.766302i	$0.722095\pi$
$410$		0			0
$411$	280.810	−	280.810i	0.683235	−	0.683235i
$412$	223.909	+	129.274i	0.543470	+	0.313772i
$413$	197.145	+	341.464i	0.477348	+	0.826790i
$414$	107.613	+	28.8348i	0.259935	+	0.0696493i
$415$		0			0
$416$	188.501	+	155.864i	0.453128	+	0.374672i
$417$		−	338.148i		−	0.810907i
$418$	−68.3382	−	18.3112i	−0.163489	−	0.0438066i
$419$	−335.215	−	580.610i	−0.800036	−	1.38570i	−0.919592	−	0.392876i	$-0.871480\pi$
$419$	−335.215	−	580.610i	−0.800036	−	1.38570i	0.119556	−	0.992827i	$-0.461853\pi$
$420$		0			0
$421$	3.39650	+	3.39650i	0.00806769	+	0.00806769i	0.711129	−	0.703061i	$-0.248184\pi$
$421$	3.39650	+	3.39650i	0.00806769	+	0.00806769i	−0.703061	+	0.711129i	$0.748184\pi$
$422$	25.3333	+	94.5451i	0.0600315	+	0.224040i
$423$	−384.147	+	102.932i	−0.908149	+	0.243338i
$424$	77.7692	−	77.7692i	0.183418	−	0.183418i
$425$		0			0
$426$	98.6202	−	56.9384i	0.231503	−	0.133658i
$427$	51.4029	−	191.838i	0.120382	−	0.449270i
$428$	−618.380			−1.44481
$429$	169.467	−	204.953i	0.395029	−	0.477746i
$430$		0			0
$431$	80.5022	−	300.438i	0.186780	−	0.697072i	−0.807462	−	0.589919i	$-0.799160\pi$
$431$	80.5022	−	300.438i	0.186780	−	0.697072i	0.994242	−	0.107154i	$-0.0341736\pi$
$432$	−30.6445	+	17.6926i	−0.0709364	+	0.0409551i
$433$	−135.494	+	234.682i	−0.312919	+	0.541992i	−0.978993	−	0.203894i	$-0.934640\pi$
$433$	−135.494	+	234.682i	−0.312919	+	0.541992i	0.666074	+	0.745886i	$0.267974\pi$
$434$	39.2297	+	39.2297i	0.0903910	+	0.0903910i
$435$		0			0
$436$	−53.8217	−	200.865i	−0.123444	−	0.460701i
$437$	783.647	+	783.647i	1.79324	+	1.79324i
$438$	117.658	+	67.9300i	0.268626	+	0.155091i
$439$	387.868	−	223.936i	0.883526	−	0.510104i	0.0117065	−	0.999931i	$-0.496274\pi$
$439$	387.868	−	223.936i	0.883526	−	0.510104i	0.871819	+	0.489828i	$0.162940\pi$
$440$		0			0
$441$		−	494.759i		−	1.12190i
$442$	19.8932	−	117.792i	0.0450073	−	0.266497i
$443$		−	481.226i		−	1.08629i	−0.839640	−	0.543144i	$-0.817234\pi$
$443$		−	481.226i		−	1.08629i	0.839640	−	0.543144i	$-0.182766\pi$
$444$	−61.4977	+	229.513i	−0.138508	+	0.516920i
$445$		0			0
$446$	−75.9264	−	43.8361i	−0.170239	−	0.0982873i
$447$	16.4133	−	16.4133i	0.0367188	−	0.0367188i
$448$	129.096	+	481.793i	0.288161	+	1.07543i
$449$	179.105	+	668.430i	0.398898	+	1.48871i	0.815038	+	0.579408i	$0.196716\pi$
$449$	179.105	+	668.430i	0.398898	+	1.48871i	−0.416139	+	0.909301i	$0.636617\pi$
$450$		0			0
$451$	35.0259	−	60.6667i	0.0776628	−	0.134516i
$452$	169.546	+	293.662i	0.375101	+	0.649694i
$453$	−213.586	+	797.114i	−0.471493	+	1.75963i
$454$			42.3516i			0.0932854i
$455$		0			0
$456$	−470.799			−1.03245
$457$	645.616	+	172.992i	1.41273	+	0.378539i	0.882897	−	0.469566i	$-0.155590\pi$
$457$	645.616	+	172.992i	1.41273	+	0.378539i	0.529828	+	0.848105i	$0.322256\pi$
$458$	54.1835	−	31.2828i	0.118305	−	0.0683031i
$459$	48.5419	+	28.0257i	0.105756	+	0.0610581i
$460$		0			0
$461$	−554.352	+	148.538i	−1.20250	+	0.322209i	−0.803815	−	0.594879i	$-0.797200\pi$
$461$	−554.352	+	148.538i	−1.20250	+	0.322209i	−0.398685	+	0.917088i	$0.630533\pi$
$462$	−85.3383	+	22.8663i	−0.184715	+	0.0494942i
$463$	−490.567	−	490.567i	−1.05954	−	1.05954i	−0.998111	−	0.0614296i	$-0.980434\pi$
$463$	−490.567	−	490.567i	−1.05954	−	1.05954i	−0.0614296	−	0.998111i	$-0.519566\pi$
$464$	−188.751	+	326.927i	−0.406791	+	0.704583i
$465$		0			0
$466$	136.159	+	36.4838i	0.292187	+	0.0782913i
$467$	−660.630			−1.41463			−0.707313	−	0.706901i	$-0.750093\pi$
$467$	−660.630			−1.41463			−0.707313	+	0.706901i	$0.750093\pi$
$468$	173.720	−	379.683i	0.371196	−	0.811289i
$469$	469.397			1.00085
$470$		0			0
$471$	38.2948	+	66.3285i	0.0813052	+	0.140825i
$472$	61.7312	−	106.922i	0.130787	−	0.226529i
$473$	−20.5832	+	20.5832i	−0.0435162	+	0.0435162i
$474$	118.949	−	31.8723i	0.250947	−	0.0672411i
$475$		0			0
$476$	621.635	−	621.635i	1.30596	−	1.30596i
$477$	−245.685	−	141.846i	−0.515063	−	0.297372i
$478$	−59.2671	−	102.654i	−0.123990	−	0.214757i
$479$	100.331	+	26.8837i	0.209460	+	0.0561246i	0.362023	−	0.932169i	$-0.382086\pi$
$479$	100.331	+	26.8837i	0.209460	+	0.0561246i	−0.152563	+	0.988294i	$0.548753\pi$
$480$		0			0
$481$	67.5033	+	181.375i	0.140340	+	0.377078i
$482$		−	112.968i		−	0.234373i
$483$	1336.78	+	358.189i	2.76766	+	0.741592i
$484$	185.502	+	321.298i	0.383268	+	0.663839i
$485$		0			0
$486$	−98.8312	−	98.8312i	−0.203356	−	0.203356i
$487$	−166.791	−	622.473i	−0.342487	−	1.27818i	−0.895521	−	0.445020i	$-0.853197\pi$
$487$	−166.791	−	622.473i	−0.342487	−	1.27818i	0.553034	−	0.833159i	$-0.313470\pi$
$488$	−60.0697	+	16.0956i	−0.123094	+	0.0329829i
$489$	188.490	−	188.490i	0.385460	−	0.385460i
$490$		0			0
$491$	−739.050	+	426.691i	−1.50519	+	0.869024i	−0.505213	+	0.862995i	$0.668586\pi$
$491$	−739.050	+	426.691i	−1.50519	+	0.869024i	−0.999982	+	0.00602943i	$0.998081\pi$
$492$	58.9941	−	220.169i	0.119907	−	0.447498i
$493$	597.976			1.21293
$494$	−152.808	+	108.651i	−0.309328	+	0.219942i
$495$		0			0
$496$	−46.4033	+	173.179i	−0.0935550	+	0.349152i
$497$	591.124	−	341.286i	1.18938	−	0.686691i
$498$	−66.2135	+	114.685i	−0.132959	+	0.230292i
$499$	−295.973	−	295.973i	−0.593133	−	0.593133i	0.345343	−	0.938476i	$-0.387763\pi$
$499$	−295.973	−	295.973i	−0.593133	−	0.593133i	−0.938476	+	0.345343i	$0.887763\pi$
$500$		0			0
$501$	279.361	+	1042.59i	0.557607	+	2.08102i
$502$	73.1363	+	73.1363i	0.145690	+	0.145690i
$503$	398.014	+	229.793i	0.791280	+	0.456846i	0.840413	−	0.541947i	$-0.182313\pi$
$503$	398.014	+	229.793i	0.791280	+	0.456846i	−0.0491332	+	0.998792i	$0.515646\pi$
$504$	−245.677	+	141.842i	−0.487454	+	0.281432i
$505$		0			0
$506$		−	65.1209i		−	0.128697i
$507$	−132.405	−	692.245i	−0.261154	−	1.36538i
$508$		−	589.205i		−	1.15985i
$509$	75.4090	−	281.430i	0.148151	−	0.552908i	−0.851444	−	0.524446i	$-0.824272\pi$
$509$	75.4090	−	281.430i	0.148151	−	0.552908i	0.999595	−	0.0284619i	$-0.00906091\pi$
$510$		0			0
$511$	705.237	+	407.169i	1.38011	+	0.796807i
$512$	314.111	−	314.111i	0.613498	−	0.613498i
$513$	−22.7696	−	84.9775i	−0.0443853	−	0.165648i
$514$	31.3094	+	116.848i	0.0609132	+	0.227331i
$515$		0			0
$516$	−47.3576	+	82.0257i	−0.0917783	+	0.158965i
$517$	116.231	+	201.319i	0.224819	+	0.389398i
$518$	16.6401	−	62.1017i	0.0321238	−	0.119888i
$519$			1181.06i			2.27564i
$520$		0			0
$521$	209.213			0.401561			0.200780	−	0.979636i	$-0.435652\pi$
$521$	209.213			0.401561			0.200780	+	0.979636i	$0.435652\pi$
$522$	−91.1353	−	24.4196i	−0.174589	−	0.0467809i
$523$	−115.597	+	66.7400i	−0.221027	+	0.127610i	−0.606426	−	0.795140i	$-0.707397\pi$
$523$	−115.597	+	66.7400i	−0.221027	+	0.127610i	0.385399	+	0.922750i	$0.374064\pi$
$524$	−478.414	−	276.213i	−0.913004	−	0.527123i
$525$		0			0
$526$	−1.17557	+	0.314992i	−0.00223492	+	0.000598844i
$527$	274.322	−	73.5042i	0.520534	−	0.139477i
$528$	−201.887	−	201.887i	−0.382361	−	0.382361i
$529$	−245.542	+	425.292i	−0.464163	+	0.803954i
$530$		0			0
$531$	−307.613	−	82.4246i	−0.579308	−	0.155225i
$532$	−1379.83			−2.59366
$533$	−64.7552	−	173.991i	−0.121492	−	0.326437i
$534$	−119.985			−0.224691
$535$		0			0
$536$	−73.4904	−	127.289i	−0.137109	−	0.237480i
$537$	−654.464	+	1133.56i	−1.21874	+	2.11092i
$538$	39.2356	−	39.2356i	0.0729286	−	0.0729286i
$539$	−279.342	+	74.8495i	−0.518260	+	0.138867i
$540$		0			0
$541$	−67.8052	+	67.8052i	−0.125333	+	0.125333i	−0.766991	−	0.641658i	$-0.778247\pi$
$541$	−67.8052	+	67.8052i	−0.125333	+	0.125333i	0.641658	+	0.766991i	$0.278247\pi$
$542$	167.980	+	96.9833i	0.309926	+	0.178936i
$543$	−619.197	−	1072.48i	−1.14033	−	1.97510i
$544$	−401.781	−	107.657i	−0.738568	−	0.197899i
$545$		0			0
$546$	−97.4159	+	212.913i	−0.178417	+	0.389950i
$547$			119.315i			0.218127i	0.994035	+	0.109063i	$0.0347852\pi$
$547$			119.315i			0.218127i	−0.994035	+	0.109063i	$0.965215\pi$
$548$	−352.030	−	94.3262i	−0.642391	−	0.172128i
$549$	80.2061	+	138.921i	0.146095	+	0.253044i
$550$		0			0
$551$	−663.655	−	663.655i	−1.20446	−	1.20446i
$552$	−112.159	−	418.581i	−0.203186	−	0.758300i
$553$	712.973	−	191.041i	1.28928	−	0.345462i
$554$	39.8528	−	39.8528i	0.0719365	−	0.0719365i
$555$		0			0
$556$	−268.749	+	155.162i	−0.483362	+	0.279069i
$557$	−25.5260	+	95.2642i	−0.0458276	+	0.171031i	−0.985047	−	0.172287i	$-0.944884\pi$
$557$	−25.5260	+	95.2642i	−0.0458276	+	0.171031i	0.939219	+	0.343318i	$0.111551\pi$
$558$	−44.8101			−0.0803048
$559$	7.27875	+	76.8000i	0.0130210	+	0.137388i
$560$		0			0
$561$	−117.053	+	436.848i	−0.208651	+	0.778695i
$562$	−180.334	+	104.116i	−0.320879	+	0.185260i
$563$	−116.005	+	200.926i	−0.206047	+	0.356884i	−0.950466	−	0.310829i	$-0.899393\pi$
$563$	−116.005	+	200.926i	−0.206047	+	0.356884i	0.744419	+	0.667713i	$0.232727\pi$
$564$	534.848	+	534.848i	0.948313	+	0.948313i
$565$		0			0
$566$	6.29519	+	23.4940i	0.0111222	+	0.0415088i
$567$	−632.587	−	632.587i	−1.11567	−	1.11567i
$568$	−185.097	−	106.866i	−0.325874	−	0.188144i
$569$	426.129	−	246.026i	0.748909	−	0.432383i	−0.0763909	−	0.997078i	$-0.524340\pi$
$569$	426.129	−	246.026i	0.748909	−	0.432383i	0.825299	+	0.564695i	$0.191006\pi$
$570$		0			0
$571$		−	10.1849i		−	0.0178370i	−0.999960	−	0.00891851i	$-0.997161\pi$
$571$		−	10.1849i		−	0.0178370i	0.999960	−	0.00891851i	$-0.00283889\pi$
$572$	−240.651	−	40.6424i	−0.420719	−	0.0710532i
$573$			1307.88i			2.28251i
$574$	−15.9627	+	59.5735i	−0.0278095	+	0.103787i
$575$		0			0
$576$	−348.894	−	201.434i	−0.605718	−	0.349712i
$577$	−116.939	+	116.939i	−0.202667	+	0.202667i	−0.801142	−	0.598475i	$-0.795774\pi$
$577$	−116.939	+	116.939i	−0.202667	+	0.202667i	0.598475	+	0.801142i	$0.295774\pi$
$578$	21.4891	+	80.1984i	0.0371783	+	0.138751i
$579$	−97.2071	−	362.782i	−0.167888	−	0.626566i
$580$		0			0
$581$	−396.880	+	687.416i	−0.683098	+	1.18316i
$582$	49.6643	+	86.0211i	0.0853339	+	0.147803i
$583$	−42.9184	+	160.174i	−0.0736165	+	0.274741i
$584$		−	254.991i		−	0.436628i
$585$		0			0
$586$	−1.88487			−0.00321650
$587$	−1016.36	−	272.333i	−1.73145	−	0.463940i	−0.750932	−	0.660379i	$-0.770396\pi$
$587$	−1016.36	−	272.333i	−1.73145	−	0.463940i	−0.980516	+	0.196439i	$0.937062\pi$
$588$	−814.922	+	470.495i	−1.38592	+	0.800162i
$589$	−386.030	−	222.875i	−0.655399	−	0.378395i
$590$		0			0
$591$	−167.590	+	44.9055i	−0.283570	+	0.0759823i
$592$	200.690	−	53.7748i	0.339004	−	0.0908358i
$593$	110.395	+	110.395i	0.186163	+	0.186163i	0.794035	−	0.607872i	$-0.207977\pi$
$593$	110.395	+	110.395i	0.186163	+	0.186163i	−0.607872	+	0.794035i	$0.707977\pi$
$594$	−2.58473	+	4.47688i	−0.00435139	+	0.00753683i
$595$		0			0
$596$	−20.5762	−	5.51337i	−0.0345238	−	0.00925062i
$597$	523.639			0.877117
$598$	−133.004	−	109.975i	−0.222415	−	0.183905i
$599$	213.440			0.356327			0.178163	−	0.984001i	$-0.442984\pi$
$599$	213.440			0.356327			0.178163	+	0.984001i	$0.442984\pi$
$600$		0			0
$601$	373.758	+	647.369i	0.621894	+	1.07715i	0.989133	+	0.147026i	$0.0469700\pi$
$601$	373.758	+	647.369i	0.621894	+	1.07715i	−0.367238	+	0.930127i	$0.619697\pi$
$602$	12.8141	−	22.1946i	0.0212858	−	0.0368681i
$603$	−268.084	+	268.084i	−0.444584	+	0.444584i
$604$	731.526	−	196.012i	1.21114	−	0.324523i
$605$		0			0
$606$	−131.711	+	131.711i	−0.217345	+	0.217345i
$607$	−46.3518	−	26.7612i	−0.0763621	−	0.0440877i	0.461333	−	0.887227i	$-0.347371\pi$
$607$	−46.3518	−	26.7612i	−0.0763621	−	0.0440877i	−0.537695	+	0.843140i	$0.680705\pi$
$608$	326.430	+	565.393i	0.536891	+	0.929923i
$609$	−1132.09	−	303.343i	−1.85894	−	0.498100i
$610$		0			0
$611$	607.466	+	102.592i	0.994217	+	0.167908i
$612$			710.062i			1.16023i
$613$	456.180	+	122.233i	0.744176	+	0.199401i	0.610933	−	0.791682i	$-0.290794\pi$
$613$	456.180	+	122.233i	0.744176	+	0.199401i	0.133243	+	0.991083i	$0.457461\pi$
$614$	−51.1672	−	88.6242i	−0.0833342	−	0.144339i
$615$		0			0
$616$	117.251	+	117.251i	0.190343	+	0.190343i
$617$	11.2003	+	41.7999i	0.0181528	+	0.0677470i	0.974408	−	0.224786i	$-0.0721684\pi$
$617$	11.2003	+	41.7999i	0.0181528	+	0.0677470i	−0.956255	+	0.292533i	$0.905502\pi$
$618$	113.113	−	30.3084i	0.183030	−	0.0490428i
$619$	401.379	−	401.379i	0.648431	−	0.648431i	−0.304183	−	0.952614i	$-0.598383\pi$
$619$	401.379	−	401.379i	0.648431	−	0.648431i	0.952614	+	0.304183i	$0.0983833\pi$
$620$		0			0
$621$	70.1279	−	40.4884i	0.112927	−	0.0651987i
$622$	17.4819	−	65.2433i	0.0281059	−	0.104893i
$623$	−719.182			−1.15439
$624$	−753.281	+	71.3925i	−1.20718	+	0.114411i
$625$		0			0
$626$	33.1425	−	123.689i	0.0529432	−	0.197587i
$627$	614.740	−	354.920i	0.980446	−	0.566061i
$628$	35.1438	−	60.8708i	0.0559614	−	0.0969280i
$629$	−232.719	−	232.719i	−0.369982	−	0.369982i
$630$		0			0
$631$	−99.4657	−	371.211i	−0.157632	−	0.588290i	−0.998866	−	0.0476184i	$-0.984837\pi$
$631$	−99.4657	−	371.211i	−0.157632	−	0.588290i	0.841234	−	0.540672i	$-0.181830\pi$
$632$	−163.431	−	163.431i	−0.258593	−	0.258593i
$633$	−850.485	−	491.028i	−1.34358	−	0.775715i
$634$	−16.3998	+	9.46841i	−0.0258671	+	0.0149344i
$635$		0			0
$636$			539.560i			0.848365i
$637$	−318.876	+	696.938i	−0.500591	+	1.09409i
$638$			55.1496i			0.0864413i
$639$	−142.689	+	532.522i	−0.223300	+	0.833367i
$640$		0			0
$641$	853.969	+	493.039i	1.33224	+	0.769172i	0.985643	−	0.168841i	$-0.0540024\pi$
$641$	853.969	+	493.039i	1.33224	+	0.769172i	0.346601	+	0.938013i	$0.387336\pi$
$642$	−198.046	+	198.046i	−0.308483	+	0.308483i
$643$	−119.238	−	445.003i	−0.185441	−	0.692073i	−0.994536	−	0.104396i	$-0.966709\pi$
$643$	−119.238	−	445.003i	−0.185441	−	0.692073i	0.809095	−	0.587677i	$-0.199958\pi$
$644$	−328.716	−	1226.79i	−0.510429	−	1.90495i
$645$		0			0
$646$	159.428	−	276.138i	0.246793	−	0.427458i
$647$	−502.801	−	870.876i	−0.777126	−	1.34602i	−0.933592	−	0.358339i	$-0.883343\pi$
$647$	−502.801	−	870.876i	−0.777126	−	1.34602i	0.156465	−	0.987683i	$-0.449990\pi$
$648$	−72.5023	+	270.582i	−0.111886	+	0.417565i
$649$			186.149i			0.286824i
$650$		0			0
$651$	−556.635			−0.855047
$652$	−236.296	−	63.3153i	−0.362417	−	0.0971094i
$653$	956.041	−	551.971i	1.46408	−	0.845285i	0.464880	−	0.885374i	$-0.346098\pi$
$653$	956.041	−	551.971i	1.46408	−	0.845285i	0.999196	+	0.0400894i	$0.0127643\pi$
$654$	−81.5676	−	47.0931i	−0.124721	−	0.0720078i
$655$		0			0
$656$	−192.520	+	51.5856i	−0.293475	+	0.0786365i
$657$	−635.321	+	170.234i	−0.967004	+	0.259108i
$658$	−144.720	−	144.720i	−0.219939	−	0.219939i
$659$	−68.1072	+	117.965i	−0.103349	+	0.179006i	−0.913063	−	0.407819i	$-0.866289\pi$
$659$	−68.1072	+	117.965i	−0.103349	+	0.179006i	0.809713	+	0.586826i	$0.199623\pi$
$660$		0			0
$661$	−1064.36	−	285.195i	−1.61023	−	0.431460i	−0.662118	−	0.749400i	$-0.730342\pi$
$661$	−1064.36	−	285.195i	−1.61023	−	0.431460i	−0.948111	+	0.317940i	$0.897009\pi$
$662$	−48.7205			−0.0735959
$663$	694.547	+	976.815i	1.04758	+	1.47333i
$664$	248.547			0.374319
$665$		0			0
$666$	25.9642	+	44.9714i	0.0389853	+	0.0675246i
$667$	431.945	−	748.150i	0.647593	−	1.12166i
$668$	700.429	−	700.429i	1.04855	−	1.04855i
$669$	849.663	−	227.666i	1.27005	−	0.340309i
$670$		0			0
$671$	66.3012	−	66.3012i	0.0988096	−	0.0988096i
$672$	706.043	+	407.634i	1.05066	+	0.606598i
$673$	−405.466	−	702.287i	−0.602475	−	1.04352i	−0.992445	−	0.122690i	$-0.960848\pi$
$673$	−405.466	−	702.287i	−0.602475	−	1.04352i	0.389970	−	0.920828i	$-0.372485\pi$
$674$	98.2857	+	26.3356i	0.145825	+	0.0390736i
$675$		0			0
$676$	−489.418	+	422.874i	−0.723992	+	0.625553i
$677$		−	991.454i		−	1.46448i	−0.681046	−	0.732241i	$-0.738475\pi$
$677$		−	991.454i		−	1.46448i	0.681046	−	0.732241i	$-0.261525\pi$
$678$	148.350	+	39.7501i	0.218805	+	0.0586285i
$679$	297.685	+	515.606i	0.438417	+	0.759361i
$680$		0			0
$681$	−300.466	−	300.466i	−0.441213	−	0.441213i
$682$	6.77909	+	25.2999i	0.00994001	+	0.0370966i
$683$	575.729	−	154.266i	0.842942	−	0.225866i	0.188590	−	0.982056i	$-0.439608\pi$
$683$	575.729	−	154.266i	0.842942	−	0.225866i	0.654352	+	0.756190i	$0.272942\pi$
$684$	788.053	−	788.053i	1.15212	−	1.15212i
$685$		0			0
$686$	37.2355	−	21.4979i	0.0542791	−	0.0313381i
$687$	−162.470	+	606.346i	−0.236492	+	0.882600i
$688$	82.8208			0.120379
$689$	254.661	+	358.157i	0.369610	+	0.519821i
$690$		0			0
$691$	217.171	−	810.493i	0.314285	−	1.17293i	−0.610368	−	0.792118i	$-0.708979\pi$
$691$	217.171	−	810.493i	0.314285	−	1.17293i	0.924653	−	0.380810i	$-0.124355\pi$
$692$	938.667	−	541.939i	1.35645	−	0.783150i
$693$	213.859	−	370.415i	0.308599	−	0.534510i
$694$	19.8358	+	19.8358i	0.0285818	+	0.0285818i
$695$		0			0
$696$	94.9849	+	354.488i	0.136472	+	0.509322i
$697$	223.244	+	223.244i	0.320293	+	0.320293i
$698$	−152.911	−	88.2830i	−0.219070	−	0.126480i
$699$	−1224.83	+	707.154i	−1.75226	+	1.01167i
$700$		0			0
$701$		−	428.642i		−	0.611472i	−0.952116	−	0.305736i	$-0.901097\pi$
$701$		−	428.642i		−	0.611472i	0.952116	−	0.305736i	$-0.0989026\pi$
$702$	4.77858	+	12.8396i	0.00680710	+	0.0182900i
$703$			516.560i			0.734793i
$704$	−60.9478	+	227.460i	−0.0865736	+	0.323097i
$705$		0			0
$706$	−24.5980	−	14.2017i	−0.0348414	−	0.0201157i
$707$	−789.467	+	789.467i	−1.11664	+	1.11664i
$708$	156.765	+	585.054i	0.221419	+	0.826347i
$709$	70.5186	+	263.179i	0.0994620	+	0.371197i	0.997658	−	0.0683976i	$-0.0217887\pi$
$709$	70.5186	+	263.179i	0.0994620	+	0.371197i	−0.898196	+	0.439595i	$0.855122\pi$
$710$		0			0
$711$	−298.088	+	516.304i	−0.419252	+	0.726166i
$712$	112.598	+	195.025i	0.158143	+	0.273911i
$713$	106.191	−	396.310i	0.148935	−	0.555834i
$714$		−	398.177i		−	0.557671i
$715$		0			0
$716$	1201.23			1.67769
$717$	1148.76	+	307.809i	1.60217	+	0.429301i
$718$	40.0755	−	23.1376i	0.0558155	−	0.0322251i
$719$	320.554	+	185.072i	0.445833	+	0.257402i	0.706069	−	0.708143i	$-0.250467\pi$
$719$	320.554	+	185.072i	0.445833	+	0.257402i	−0.260236	+	0.965545i	$0.583800\pi$
$720$		0			0
$721$	677.991	−	181.667i	0.940348	−	0.251965i
$722$	−338.469	+	90.6925i	−0.468793	+	0.125613i
$723$	801.457	+	801.457i	1.10852	+	1.10852i
$724$	−568.248	+	984.234i	−0.784873	+	1.35944i
$725$		0			0
$726$	162.311	+	43.4910i	0.223568	+	0.0599050i
$727$	1190.04			1.63692			0.818458	−	0.574566i	$-0.194829\pi$
$727$	1190.04			1.63692			0.818458	+	0.574566i	$0.194829\pi$
$728$	437.489	−	41.4632i	0.600946	−	0.0569549i
$729$	627.411			0.860646
$730$		0			0
$731$	−65.5954	−	113.614i	−0.0897337	−	0.155423i
$732$	152.545	−	264.216i	0.208395	−	0.360951i
$733$	−225.841	+	225.841i	−0.308105	+	0.308105i	−0.844174	−	0.536069i	$-0.819909\pi$
$733$	−225.841	+	225.841i	−0.308105	+	0.308105i	0.536069	+	0.844174i	$0.319909\pi$
$734$	74.8174	−	20.0472i	0.101931	−	0.0273123i
$735$		0			0
$736$	−424.918	+	424.918i	−0.577334	+	0.577334i
$737$	191.918	+	110.804i	0.260404	+	0.150345i
$738$	−24.9072	−	43.1405i	−0.0337496	−	0.0584560i
$739$	161.258	+	43.2089i	0.218211	+	0.0584694i	0.366268	−	0.930509i	$-0.380635\pi$
$739$	161.258	+	43.2089i	0.218211	+	0.0584694i	−0.148057	+	0.988979i	$0.547302\pi$
$740$		0			0
$741$	313.271	−	1854.94i	0.422768	−	2.50329i
$742$		−	145.995i		−	0.196758i
$743$	−856.091	−	229.389i	−1.15221	−	0.308734i	−0.368359	−	0.929684i	$-0.620080\pi$
$743$	−856.091	−	229.389i	−1.15221	−	0.308734i	−0.783850	+	0.620950i	$0.786747\pi$
$744$	87.1487	+	150.946i	0.117135	+	0.202884i
$745$		0			0
$746$	−44.4787	−	44.4787i	−0.0596229	−	0.0596229i
$747$	−165.932	−	619.268i	−0.222132	−	0.829007i
$748$	400.903	−	107.422i	0.535967	−	0.143612i
$749$	−1187.08	+	1187.08i	−1.58488	+	1.58488i
$750$		0			0
$751$	48.7326	−	28.1358i	0.0648903	−	0.0374644i	−0.467204	−	0.884150i	$-0.654739\pi$
$751$	48.7326	−	28.1358i	0.0648903	−	0.0374644i	0.532094	+	0.846685i	$0.321405\pi$
$752$	171.183	−	638.865i	0.227638	−	0.849555i
$753$	−1037.74			−1.37814
$754$	112.638	+	93.1360i	0.149388	+	0.123523i
$755$		0			0
$756$	−26.0943	+	97.3853i	−0.0345163	+	0.128816i
$757$	−386.198	+	222.971i	−0.510169	+	0.294546i	−0.732903	−	0.680333i	$-0.761835\pi$
$757$	−386.198	+	222.971i	−0.510169	+	0.294546i	0.222734	+	0.974879i	$0.428502\pi$
$758$	−52.1508	+	90.3278i	−0.0688005	+	0.119166i
$759$	462.004	+	462.004i	0.608701	+	0.608701i
$760$		0			0
$761$	−109.741	−	409.560i	−0.144207	−	0.538186i	−0.999789	−	0.0205203i	$-0.993468\pi$
$761$	−109.741	−	409.560i	−0.144207	−	0.538186i	0.855583	−	0.517666i	$-0.173199\pi$
$762$	−188.702	−	188.702i	−0.247641	−	0.247641i
$763$	−488.912	−	282.273i	−0.640775	−	0.369952i
$764$	1039.46	−	600.131i	1.36055	−	0.785512i
$765$		0			0
$766$		−	14.8826i		−	0.0194290i
$767$	380.193	+	314.366i	0.495688	+	0.409864i
$768$			635.763i			0.827816i
$769$	10.4219	−	38.8950i	0.0135525	−	0.0505787i	−0.958818	−	0.284020i	$-0.908332\pi$
$769$	10.4219	−	38.8950i	0.0135525	−	0.0505787i	0.972371	+	0.233441i	$0.0749986\pi$
$770$		0			0
$771$	−1051.11	−	606.861i	−1.36331	−	0.787109i
$772$	−243.723	+	243.723i	−0.315703	+	0.315703i
$773$	−270.055	−	1007.86i	−0.349360	−	1.30383i	−0.887436	−	0.460932i	$-0.847515\pi$
$773$	−270.055	−	1007.86i	−0.349360	−	1.30383i	0.538076	−	0.842896i	$-0.319151\pi$
$774$	5.35746	+	19.9943i	0.00692178	+	0.0258324i
$775$		0			0
$776$	93.2132	−	161.450i	0.120120	−	0.208054i
$777$	322.530	+	558.639i	0.415097	+	0.718969i
$778$	4.12017	−	15.3767i	0.00529585	−	0.0197644i
$779$		−	495.530i		−	0.636110i
$780$		0			0
$781$	322.250			0.412612
$782$	283.491	+	75.9613i	0.362521	+	0.0971372i
$783$	−59.3899	+	34.2888i	−0.0758492	+	0.0437916i
$784$	712.583	+	411.410i	0.908907	+	0.524758i
$785$		0			0
$786$	−241.681	+	64.7583i	−0.307482	+	0.0823896i
$787$	−138.586	+	37.1339i	−0.176094	+	0.0471842i	−0.345788	−	0.938313i	$-0.612389\pi$
$787$	−138.586	+	37.1339i	−0.176094	+	0.0471842i	0.169695	+	0.985497i	$0.445722\pi$
$788$	112.589	+	112.589i	0.142880	+	0.142880i
$789$	6.10540	−	10.5749i	0.00773815	−	0.0134029i
$790$		0			0
$791$	889.199	+	238.260i	1.12414	+	0.301214i
$792$	−133.930			−0.169104
$793$	−23.4459	−	247.383i	−0.0295660	−	0.311959i
$794$	−68.9980			−0.0868993
$795$		0			0
$796$	−240.276	−	416.171i	−0.301855	−	0.522827i
$797$	80.3553	−	139.179i	0.100822	−	0.174629i	−0.811201	−	0.584767i	$-0.801186\pi$
$797$	80.3553	−	139.179i	0.100822	−	0.174629i	0.912024	+	0.410138i	$0.134519\pi$
$798$	−441.912	+	441.912i	−0.553774	+	0.553774i
$799$	−1011.98	+	271.160i	−1.26656	+	0.339374i
$800$		0			0
$801$	410.742	−	410.742i	0.512787	−	0.512787i
$802$	35.0915	+	20.2601i	0.0437550	+	0.0252619i
$803$	192.229	+	332.951i	0.239389	+	0.414633i
$804$	696.501	+	186.627i	0.866294	+	0.232123i
$805$		0			0
$806$	63.1213	+	28.8805i	0.0783143	+	0.0358319i
$807$			556.719i			0.689862i
$808$	337.686	+	90.4827i	0.417928	+	0.111984i
$809$	−493.689	−	855.095i	−0.610246	−	1.05698i	−0.991199	−	0.132383i	$-0.957737\pi$
$809$	−493.689	−	855.095i	−0.610246	−	1.05698i	0.380952	−	0.924595i	$-0.375596\pi$
$810$		0			0
$811$	658.494	+	658.494i	0.811953	+	0.811953i	0.984927	−	0.172973i	$-0.0553374\pi$
$811$	658.494	+	658.494i	0.811953	+	0.811953i	−0.172973	+	0.984927i	$0.555337\pi$
$812$	278.383	+	1038.94i	0.342837	+	1.27948i
$813$	−1879.80	+	503.691i	−2.31218	+	0.619546i
$814$	21.4630	−	21.4630i	0.0263673	−	0.0263673i
$815$		0			0
$816$	1114.37	−	643.382i	1.36565	−	0.788458i
$817$	−53.2934	+	198.894i	−0.0652306	+	0.243444i
$818$	278.439			0.340391
$819$	−395.379	−	1062.34i	−0.482758	−	1.29712i
$820$		0			0
$821$	−180.926	+	675.225i	−0.220373	+	0.822442i	0.763833	+	0.645414i	$0.223315\pi$
$821$	−180.926	+	675.225i	−0.220373	+	0.822442i	−0.984206	+	0.177028i	$0.943352\pi$
$822$	−142.953	+	82.5337i	−0.173908	+	0.100406i
$823$	−591.929	+	1025.25i	−0.719233	+	1.24575i	0.242071	+	0.970259i	$0.422173\pi$
$823$	−591.929	+	1025.25i	−0.719233	+	1.24575i	−0.961304	+	0.275490i	$0.911160\pi$
$824$	−155.412	−	155.412i	−0.188607	−	0.188607i
$825$		0			0
$826$	−42.4176	−	158.305i	−0.0513530	−	0.191652i
$827$	193.163	+	193.163i	0.233571	+	0.233571i	0.814182	−	0.580610i	$-0.197186\pi$
$827$	193.163	+	193.163i	0.233571	+	0.233571i	−0.580610	+	0.814182i	$0.697186\pi$
$828$	888.385	+	512.909i	1.07293	+	0.619456i
$829$	984.729	−	568.534i	1.18785	−	0.685807i	0.230034	−	0.973183i	$-0.426116\pi$
$829$	984.729	−	568.534i	1.18785	−	0.685807i	0.957818	+	0.287376i	$0.0927829\pi$
$830$		0			0
$831$			565.477i			0.680478i
$832$	361.641	+	508.613i	0.434664	+	0.611314i
$833$		−	1303.37i		−	1.56467i
$834$	−36.3779	+	135.764i	−0.0436186	+	0.162787i
$835$		0			0
$836$	−564.157	−	325.716i	−0.674830	−	0.389613i
$837$	−23.0303	+	23.0303i	−0.0275153	+	0.0275153i
$838$	72.1248	+	269.173i	0.0860677	+	0.321209i
$839$	−418.360	−	1561.34i	−0.498642	−	1.86096i	−0.508596	−	0.861005i	$-0.669835\pi$
$839$	−418.360	−	1561.34i	−0.498642	−	1.86096i	0.00995455	−	0.999950i	$-0.496831\pi$
$840$		0			0
$841$	54.6947	−	94.7341i	0.0650354	−	0.112645i
$842$	−0.998277	−	1.72907i	−0.00118560	−	0.00205352i
$843$	540.734	−	2018.05i	0.641440	−	2.39389i
$844$			901.249i			1.06783i
$845$		0			0
$846$	165.306			0.195397
$847$	972.881	+	260.683i	1.14862	+	0.307772i
$848$	408.593	−	235.901i	0.481831	−	0.278185i
$849$	−211.341	−	122.018i	−0.248929	−	0.143719i
$850$		0			0
$851$	−459.266	+	123.060i	−0.539678	+	0.144606i
$852$	1012.81	−	271.382i	1.18875	−	0.318524i
$853$	−830.014	−	830.014i	−0.973053	−	0.973053i	0.0265931	−	0.999646i	$-0.491534\pi$
$853$	−830.014	−	830.014i	−0.973053	−	0.973053i	−0.999646	+	0.0265931i	$0.991534\pi$
$854$	−41.2759	+	71.4919i	−0.0483324	+	0.0837142i
$855$		0			0
$856$	507.758	+	136.053i	0.593176	+	0.158941i
$857$	−112.086			−0.130789			−0.0653946	−	0.997859i	$-0.520831\pi$
$857$	−112.086			−0.130789			−0.0653946	+	0.997859i	$0.520831\pi$
$858$	−90.0888	+	64.0561i	−0.104999	+	0.0746574i
$859$	−111.015			−0.129237			−0.0646187	−	0.997910i	$-0.520583\pi$
$859$	−111.015			−0.129237			−0.0646187	+	0.997910i	$0.520583\pi$
$860$		0			0
$861$	−309.400	−	535.896i	−0.359349	−	0.622411i
$862$	−64.6422	+	111.964i	−0.0749909	+	0.129888i
$863$	−223.632	+	223.632i	−0.259134	+	0.259134i	−0.824702	−	0.565568i	$-0.808657\pi$
$863$	−223.632	+	223.632i	−0.259134	+	0.259134i	0.565568	+	0.824702i	$0.308657\pi$
$864$	46.0774	−	12.3464i	0.0533304	−	0.0142898i
$865$		0			0
$866$	79.6470	−	79.6470i	0.0919712	−	0.0919712i
$867$	−721.428	−	416.517i	−0.832097	−	0.480411i
$868$	255.417	+	442.395i	0.294259	+	0.509672i
$869$	336.603	+	90.1925i	0.387345	+	0.103789i
$870$		0			0
$871$	550.417	−	204.852i	0.631937	−	0.235192i
$872$			176.775i			0.202723i
$873$	−464.490	−	124.460i	−0.532062	−	0.142566i
$874$	−230.325	−	398.934i	−0.263529	−	0.456446i
$875$		0			0
$876$	884.558	+	884.558i	1.00977	+	1.00977i
$877$	−353.391	−	1318.88i	−0.402955	−	1.50385i	−0.807796	−	0.589461i	$-0.799340\pi$
$877$	−353.391	−	1318.88i	−0.402955	−	1.50385i	0.404842	−	0.914387i	$-0.367327\pi$
$878$	−179.817	+	48.1819i	−0.204803	+	0.0548769i
$879$	13.3723	−	13.3723i	0.0152131	−	0.0152131i
$880$		0			0
$881$	−113.969	+	65.7999i	−0.129363	+	0.0746878i	−0.563285	−	0.826263i	$-0.690463\pi$
$881$	−113.969	+	65.7999i	−0.129363	+	0.0746878i	0.433922	+	0.900950i	$0.357129\pi$
$882$	−53.2261	+	198.642i	−0.0603470	+	0.225218i
$883$	−36.4439			−0.0412728			−0.0206364	−	0.999787i	$-0.506569\pi$
$883$	−36.4439			−0.0412728			−0.0206364	+	0.999787i	$0.506569\pi$
$884$	457.641	−	1000.22i	0.517693	−	1.13147i
$885$		0			0
$886$	−51.7702	+	193.209i	−0.0584314	+	0.218069i
$887$	−606.237	+	350.011i	−0.683469	+	0.394601i	−0.801161	−	0.598449i	$-0.795784\pi$
$887$	−606.237	+	350.011i	−0.683469	+	0.394601i	0.117691	+	0.993050i	$0.462451\pi$
$888$	100.993	−	174.925i	0.113731	−	0.196987i
$889$	−1131.07	−	1131.07i	−1.27229	−	1.27229i
$890$		0			0
$891$	−109.314	−	407.966i	−0.122687	−	0.457875i
$892$	−570.817	−	570.817i	−0.639929	−	0.639929i
$893$	1424.08	+	822.192i	1.59471	+	0.920708i
$894$	−8.35558	+	4.82410i	−0.00934629	+	0.00539608i
$895$		0			0
$896$		−	989.286i		−	1.10411i
$897$	1723.83	−	163.377i	1.92178	−	0.182137i
$898$		−	287.639i		−	0.320310i
$899$	−89.9309	+	335.627i	−0.100034	+	0.373333i
$900$		0			0
$901$	−647.223	−	373.674i	−0.718339	−	0.414733i
$902$	−20.5892	+	20.5892i	−0.0228262	+	0.0228262i
$903$	66.5509	+	248.371i	0.0736998	+	0.275051i
$904$	−74.6056	−	278.432i	−0.0825283	−	0.308000i
$905$		0			0
$906$	171.507	−	297.059i	0.189301	−	0.327879i
$907$	−131.036	−	226.961i	−0.144472	−	0.250233i	0.784704	−	0.619871i	$-0.212815\pi$
$907$	−131.036	−	226.961i	−0.144472	−	0.250233i	−0.929176	+	0.369638i	$0.879482\pi$
$908$	−100.929	+	376.672i	−0.111155	+	0.414837i
$909$		−	901.768i		−	0.992044i
$910$		0			0
$911$	498.041			0.546697			0.273349	−	0.961915i	$-0.411869\pi$
$911$	498.041			0.546697			0.273349	+	0.961915i	$0.411869\pi$
$912$	−1950.82	−	522.720i	−2.13905	−	0.573158i
$913$	−324.537	+	187.372i	−0.355463	+	0.205226i
$914$	−240.600	−	138.910i	−0.263238	−	0.151981i
$915$		0			0
$916$	556.455	−	149.102i	0.607483	−	0.162775i
$917$	−1448.62	+	388.157i	−1.57974	+	0.423290i
$918$	−16.4742	−	16.4742i	−0.0179458	−	0.0179458i
$919$	133.939	−	231.989i	0.145744	−	0.252437i	−0.783906	−	0.620880i	$-0.786776\pi$
$919$	133.939	−	231.989i	0.145744	−	0.252437i	0.929650	+	0.368443i	$0.120109\pi$
$920$		0			0
$921$	991.759	+	265.741i	1.07683	+	0.288535i
$922$	238.549			0.258729
$923$	544.212	−	658.168i	0.589612	−	0.713075i
$924$	−813.486			−0.880396
$925$		0			0
$926$	144.184	+	249.735i	0.155707	+	0.269692i
$927$	−283.462	+	490.971i	−0.305785	+	0.529635i
$928$	359.855	−	359.855i	0.387774	−	0.387774i
$929$	530.823	−	142.234i	0.571392	−	0.153104i	0.0384570	−	0.999260i	$-0.487756\pi$
$929$	530.823	−	142.234i	0.571392	−	0.153104i	0.532935	+	0.846156i	$0.321089\pi$
$930$		0			0
$931$	−1446.53	+	1446.53i	−1.55374	+	1.55374i
$932$	1124.05	+	648.968i	1.20606	+	0.696318i
$933$	338.846	+	586.899i	0.363179	+	0.629045i
$934$	265.239	+	71.0705i	0.283982	+	0.0760926i
$935$		0			0
$936$	−226.180	+	273.541i	−0.241645	+	0.292245i
$937$			1688.18i			1.80169i	0.434143	+	0.900844i	$0.357051\pi$
$937$			1688.18i			1.80169i	−0.434143	+	0.900844i	$0.642949\pi$
$938$	−188.460	−	50.4977i	−0.200917	−	0.0538355i
$939$	642.391	+	1112.65i	0.684122	+	1.18493i
$940$		0			0
$941$	560.333	+	560.333i	0.595466	+	0.595466i	0.939103	−	0.343637i	$-0.111659\pi$
$941$	560.333	+	560.333i	0.595466	+	0.595466i	−0.343637	+	0.939103i	$0.611659\pi$
$942$	−8.23949	−	30.7502i	−0.00874680	−	0.0326435i
$943$	440.569	−	118.050i	0.467199	−	0.125186i
$944$	374.504	−	374.504i	0.396721	−	0.396721i
$945$		0			0
$946$	10.4783	−	6.04967i	0.0110765	−	0.00639500i
$947$	−134.844	+	503.245i	−0.142391	+	0.531410i	0.857467	+	0.514539i	$0.172037\pi$
$947$	−134.844	+	503.245i	−0.142391	+	0.531410i	−0.999858	+	0.0168706i	$0.994630\pi$
$948$	1133.88			1.19608
$949$	1004.66	+	169.672i	1.05865	+	0.178790i
$950$		0			0
$951$	49.1750	−	183.523i	0.0517087	−	0.192979i
$952$	−647.201	+	373.662i	−0.679833	+	0.392502i
$953$	−373.718	+	647.298i	−0.392149	+	0.679222i	−0.992733	−	0.120340i	$-0.961601\pi$
$953$	−373.718	+	647.298i	−0.392149	+	0.679222i	0.600584	+	0.799562i	$0.294935\pi$
$954$	83.3811	+	83.3811i	0.0874016	+	0.0874016i
$955$		0			0
$956$	−282.482	−	1054.24i	−0.295483	−	1.10276i
$957$	−391.262	−	391.262i	−0.408842	−	0.408842i
$958$	−37.3902	−	21.5873i	−0.0390295	−	0.0225337i
$959$	−856.850	+	494.703i	−0.893483	+	0.515853i
$960$		0			0
$961$		−	795.977i		−	0.828280i
$962$	−7.58987	−	80.0827i	−0.00788968	−	0.0832461i
$963$		−	1355.93i		−	1.40803i
$964$	269.216	−	1004.73i	0.279270	−	1.04225i
$965$		0			0
$966$	−498.174	−	287.621i	−0.515709	−	0.297744i
$967$	578.310	−	578.310i	0.598045	−	0.598045i	−0.341747	−	0.939792i	$-0.611019\pi$
$967$	578.310	−	578.310i	0.598045	−	0.598045i	0.939792	+	0.341747i	$0.111019\pi$
$968$	−81.6267	−	304.635i	−0.0843251	−	0.314706i
$969$	828.005	+	3090.16i	0.854494	+	3.18901i
$970$		0			0
$971$	331.204	−	573.662i	0.341096	−	0.590795i	−0.643541	−	0.765412i	$-0.722535\pi$
$971$	331.204	−	573.662i	0.341096	−	0.590795i	0.984636	+	0.174617i	$0.0558687\pi$
$972$	−643.471	−	1114.52i	−0.662007	−	1.14663i
$973$	−218.047	+	813.763i	−0.224098	+	0.836345i
$974$			267.862i			0.275012i
$975$		0			0
$976$	−266.777			−0.273337
$977$	−540.021	−	144.698i	−0.552734	−	0.148105i	−0.0283677	−	0.999598i	$-0.509031\pi$
$977$	−540.021	−	144.698i	−0.552734	−	0.148105i	−0.524366	+	0.851493i	$0.675698\pi$
$978$	−95.9552	+	55.3998i	−0.0981137	+	0.0566460i
$979$	−294.045	−	169.767i	−0.300353	−	0.173409i
$980$		0			0
$981$	440.442	−	118.016i	0.448973	−	0.120302i
$982$	342.627	−	91.8067i	0.348908	−	0.0934895i
$983$	665.030	+	665.030i	0.676532	+	0.676532i	0.959214	−	0.282682i	$-0.0912242\pi$
$983$	665.030	+	665.030i	0.676532	+	0.676532i	−0.282682	+	0.959214i	$0.591224\pi$
$984$	−96.8814	+	167.803i	−0.0984567	+	0.170532i
$985$		0			0
$986$	−240.083	−	64.3301i	−0.243492	−	0.0652435i
$987$	2053.45			2.08050
$988$	−1617.99	+	602.178i	−1.63764	+	0.609491i
$989$	−189.530			−0.191638
$990$		0			0
$991$	−325.864	−	564.412i	−0.328823	−	0.569538i	0.653456	−	0.756965i	$-0.273319\pi$
$991$	−325.864	−	564.412i	−0.328823	−	0.569538i	−0.982279	+	0.187427i	$0.939985\pi$
$992$	120.850	−	209.318i	0.121824	−	0.211006i
$993$	345.651	−	345.651i	0.348087	−	0.348087i
$994$	−274.048	+	73.4309i	−0.275702	+	0.0738741i
$995$		0			0
$996$	−862.207	+	862.207i	−0.865670	+	0.865670i
$997$	−1171.38	−	676.299i	−1.17491	−	0.678334i	−0.220078	−	0.975482i	$-0.570631\pi$
$997$	−1171.38	−	676.299i	−1.17491	−	0.678334i	−0.954831	+	0.297148i	$0.903964\pi$
$998$	86.9906	+	150.672i	0.0871650	+	0.150974i
$999$	36.4577	+	9.76880i	0.0364942	+	0.00977858i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.3.w.e.24.5		40
5.2	odd	4		65.3.p.a.11.6	yes	40
5.3	odd	4		325.3.t.d.76.5		40
5.4	even	2		325.3.w.f.24.6		40
13.6	odd	12		325.3.w.f.149.6		40
65.19	odd	12	inner	325.3.w.e.149.5		40
65.32	even	12		65.3.p.a.6.6	✓	40
65.58	even	12		325.3.t.d.201.5		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.3.p.a.6.6	✓	40	65.32	even	12
65.3.p.a.11.6	yes	40	5.2	odd	4
325.3.t.d.76.5		40	5.3	odd	4
325.3.t.d.201.5		40	65.58	even	12
325.3.w.e.24.5		40	1.1	even	1	trivial
325.3.w.e.149.5		40	65.19	odd	12	inner
325.3.w.f.24.6		40	5.4	even	2
325.3.w.f.149.6		40	13.6	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	325.w (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.401493 - 0.107580i) q^{2} +(3.61165 - 2.08519i) q^{3} +(-3.31448 - 1.91361i) q^{4} +(-1.67438 + 0.448649i) q^{6} +(-10.0361 + 2.68917i) q^{7} +(2.30053 + 2.30053i) q^{8} +(4.19603 - 7.26773i) q^{9} +(-4.73818 - 1.26959i) q^{11} -15.9610 q^{12} +(-10.5948 + 7.53326i) q^{13} +4.31874 q^{14} +(6.97830 + 12.0868i) q^{16} +(11.0538 - 19.1458i) q^{17} +(-2.46654 + 2.46654i) q^{18} +(-33.5167 + 8.98078i) q^{19} +(-30.6396 + 30.6396i) q^{21} +(1.76576 + 1.01946i) q^{22} +(-15.9694 - 27.6598i) q^{23} +(13.1058 + 3.51168i) q^{24} +(5.06417 - 1.88476i) q^{26} +2.53538i q^{27} +(38.4106 + 10.2921i) q^{28} +(13.5241 + 23.4245i) q^{29} +(9.08360 + 9.08360i) q^{31} +(-4.86966 - 18.1738i) q^{32} +(-19.7600 + 5.29467i) q^{33} +(-6.49775 + 6.49775i) q^{34} +(-27.8153 + 16.0592i) q^{36} +(3.85300 - 14.3796i) q^{37} +14.4229 q^{38} +(-22.5565 + 49.2997i) q^{39} +(-3.69614 + 13.7942i) q^{41} +(15.5978 - 9.00539i) q^{42} +(2.96708 - 5.13914i) q^{43} +(13.2751 + 13.2751i) q^{44} +(3.43597 + 12.8232i) q^{46} +(-33.5097 - 33.5097i) q^{47} +(50.4064 + 29.1022i) q^{48} +(51.0571 - 29.4778i) q^{49} -92.1974i q^{51} +(49.5320 - 4.69442i) q^{52} -33.8049i q^{53} +(0.272755 - 1.01794i) q^{54} +(-29.2749 - 16.9019i) q^{56} +(-102.324 + 102.324i) q^{57} +(-2.90985 - 10.8597i) q^{58} +(-9.82174 - 36.6552i) q^{59} +(-9.55739 + 16.5539i) q^{61} +(-2.66979 - 4.62422i) q^{62} +(-22.5677 + 84.2237i) q^{63} -48.0059i q^{64} +8.50311 q^{66} +(-43.6377 - 11.6927i) q^{67} +(-73.2755 + 42.3056i) q^{68} +(-115.352 - 66.5984i) q^{69} +(-63.4555 + 17.0028i) q^{71} +(26.3727 - 7.06654i) q^{72} +(-55.4200 - 55.4200i) q^{73} +(-3.09391 + 5.35881i) q^{74} +(128.276 + 34.3715i) q^{76} +50.9671 q^{77} +(14.3600 - 17.3669i) q^{78} -71.0406 q^{79} +(43.0510 + 74.5665i) q^{81} +(2.96795 - 5.14064i) q^{82} +(54.0196 - 54.0196i) q^{83} +(160.187 - 42.9219i) q^{84} +(-1.74413 + 1.74413i) q^{86} +(97.6891 + 56.4008i) q^{87} +(-7.97958 - 13.8210i) q^{88} +(66.8590 + 17.9148i) q^{89} +(86.0727 - 104.096i) q^{91} +122.237i q^{92} +(51.7478 + 13.8658i) q^{93} +(9.84896 + 17.0589i) q^{94} +(-55.4833 - 55.4833i) q^{96} +(-14.8307 - 55.3488i) q^{97} +(-23.6703 + 6.34244i) q^{98} +(-29.1086 + 29.1086i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 12 q^{3} - 12 q^{6} - 44 q^{7} + 36 q^{8} + 72 q^{9} - 12 q^{11} + 120 q^{12} - 36 q^{13} - 48 q^{14} + 128 q^{16} - 32 q^{17} + 136 q^{18} - 68 q^{19} - 48 q^{21} - 72 q^{22} - 28 q^{23} + 56 q^{24}+ \cdots + 76 q^{99}+O(q^{100}) \) 40 * q - 12 * q^3 - 12 * q^6 - 44 * q^7 + 36 * q^8 + 72 * q^9 - 12 * q^11 + 120 * q^12 - 36 * q^13 - 48 * q^14 + 128 * q^16 - 32 * q^17 + 136 * q^18 - 68 * q^19 - 48 * q^21 - 72 * q^22 - 28 * q^23 + 56 * q^24 - 84 * q^26 + 76 * q^28 - 28 * q^29 + 128 * q^31 + 84 * q^32 - 68 * q^33 + 28 * q^34 + 300 * q^36 - 260 * q^37 + 8 * q^38 + 88 * q^39 + 68 * q^41 - 480 * q^42 + 32 * q^43 + 240 * q^44 + 260 * q^46 - 152 * q^47 - 480 * q^48 + 132 * q^49 + 488 * q^52 - 152 * q^54 - 288 * q^56 + 252 * q^57 + 468 * q^58 - 492 * q^59 - 100 * q^61 - 8 * q^62 - 356 * q^63 - 456 * q^66 - 56 * q^67 + 12 * q^68 + 576 * q^69 - 132 * q^71 + 396 * q^72 - 424 * q^73 + 160 * q^74 - 992 * q^76 + 344 * q^77 + 12 * q^78 + 248 * q^79 + 248 * q^82 - 112 * q^83 - 1100 * q^84 + 852 * q^86 - 1068 * q^87 + 8 * q^88 - 168 * q^89 - 160 * q^91 - 24 * q^93 - 328 * q^94 + 124 * q^96 + 1020 * q^97 + 1404 * q^98 + 76 * q^99

Introduction

L-functions

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